A is a nondiagonalizable real 2×2 matrix with real eigenvalue λ and eigenvector v. Choose the general solution of y′=Ay, with arbitrary constants c₁,c₂ and (A−λI)u=v when u appears.
A single length-two Jordan chain satisfies Av=λv, Au=λu+v. Its exponential sends u to e^(λt)(u+tv). Together with e^(λt)v this gives two independent solutions. **C**.
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